| Abstract: |
| We will introduce the notion of Jacobi field over a nonholonomically constrained geodesic in a Riemmanian manifold, that extends the standard notion of Jacobi field in the absence of constraints.
The subject is of interest because some previous attempts fail to identify the proper concept of Jacobi field in the presence of constraints. In some formulations, the Jacobi field is forced to satisfy the same constraints as the geodesics. We see some examples where the Jacobi field may leave the constraint distribution. Moreover, we are able to deduce an equation to find Jacobi fields depending on a linear connection, that resembles the Jacobi equation in Riemannian geometry.
This study may be useful to study further properties of nonholonomic Lagrangian system of kinetic type, such as conjugate points or the existence of minimizing properties. |
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